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Publications
SKOLR: Structured Koopman Operator Linear RNN for Time-Series Forecasting
Koopman operator theory provides a framework for nonlinear dynamical system analysis and time-series forecasting by mapping dynamics to a sp… (voir plus)ace of real-valued measurement functions, enabling a linear operator representation. Despite the advantage of linearity, the operator is generally infinite-dimensional. Therefore, the objective is to learn measurement functions that yield a tractable finite-dimensional Koopman operator approximation. In this work, we establish a connection between Koopman operator approximation and linear Recurrent Neural Networks (RNNs), which have recently demonstrated remarkable success in sequence modeling. We show that by considering an extended state consisting of lagged observations, we can establish an equivalence between a structured Koopman operator and linear RNN updates. Building on this connection, we present SKOLR, which integrates a learnable spectral decomposition of the input signal with a multilayer perceptron (MLP) as the measurement functions and implements a structured Koopman operator via a highly parallel linear RNN stack. Numerical experiments on various forecasting benchmarks and dynamical systems show that this streamlined, Koopman-theory-based design delivers exceptional performance. Our code is available at: https://github.com/networkslab/SKOLR.
Neural network training is inherently sensitive to initialization and the randomness induced by stochastic gradient descent. However, it is … (voir plus)unclear to what extent such effects lead to meaningfully different networks, either in terms of the models' weights or the underlying functions that were learned. In this work, we show that during the initial "chaotic" phase of training, even extremely small perturbations reliably causes otherwise identical training trajectories to diverge-an effect that diminishes rapidly over training time. We quantify this divergence through (i)
Off-policy deep reinforcement learning (RL) typically leverages replay buffers for reusing past experiences during learning. This can help i… (voir plus)mprove sample efficiency when the collected data is informative and aligned with the learning objectives; when that is not the case, it can have the effect of"polluting"the replay buffer with data which can exacerbate optimization challenges in addition to wasting environment interactions due to wasteful sampling. We argue that sampling these uninformative and wasteful transitions can be avoided by addressing the sunk cost fallacy, which, in the context of deep RL, is the tendency towards continuing an episode until termination. To address this, we propose learn to stop (LEAST), a lightweight mechanism that enables strategic early episode termination based on Q-value and gradient statistics, which helps agents recognize when to terminate unproductive episodes early. We demonstrate that our method improves learning efficiency on a variety of RL algorithms, evaluated on both the MuJoCo and DeepMind Control Suite benchmarks.
The use of parallel actors for data collection has been an effective technique used in reinforcement learning (RL) algorithms. The manner in… (voir plus) which data is collected in these algorithms, controlled via the number of parallel environments and the rollout length, induces a form of bias-variance trade-off; the number of training passes over the collected data, on the other hand, must strike a balance between sample efficiency and overfitting. We conduct an empirical analysis of these trade-offs on PPO, one of the most popular RL algorithms that uses parallel actors, and establish connections to network plasticity and, more generally, optimization stability. We examine its impact on network architectures, as well as the hyper-parameter sensitivity when scaling data. Our analyses indicate that larger dataset sizes can increase final performance across a variety of settings, and that scaling parallel environments is more effective than increasing rollout lengths. These findings highlight the critical role of data collection strategies in improving agent performance.
In reinforcement learning, specifying reward functions that capture the intended task can be very challenging. Reward learning aims to addre… (voir plus)ss this issue by *learning* the reward function. However, a learned reward model may have a low error on the data distribution, and yet subsequently produce a policy with large regret. We say that such a reward model has an *error-regret mismatch*. The main source of an error-regret mismatch is the distributional shift that commonly occurs during policy optimization. In this paper, we mathematically show that a sufficiently low expected test error of the reward model guarantees low worst-case regret, but that for any *fixed* expected test error, there exist realistic data distributions that allow for error-regret mismatch to occur. We then show that similar problems persist even when using policy regularization techniques, commonly employed in methods such as RLHF. We hope our results stimulate the theoretical and empirical study of improved methods to learn reward models, and better ways to measure their quality reliably.
Compositionality is believed to be fundamental to intelligence. In humans, it underlies the structure of thought and language. In AI, it ena… (voir plus)bles a powerful form of out-of-distribution generalization, in which a model systematically adapts to novel combinations of known concepts. However, while we have strong intuitions about what compositionality is, we lack satisfying formal definitions for it. Here, we propose such a definition called representational compositionality that is conceptually simple, quantitative, and grounded in algorithmic information theory. Intuitively, representational compositionality states that a compositional representation is both expressive and describable as a simple function of parts. We validate our definition on both real and synthetic data, and show how it unifies disparate intuitions from across the literature in both AI and cognitive science. We hope that our definition can inspire the design of novel, theoretically-driven models that better capture the mechanisms of compositional thought. We make our code available at https://github.com/EricElmoznino/complexity_compositionality.
